It may be useful to compare with the results proved above, the interesting and comparatively little known properties of the Stereographic Projection of the sphere so far as they affect its practical application to spherical triangles. This projection, in which we take a point S on the sphere as the vertex of projection, and the central plane parallel to the tangent plane at S as the plane of projection, has certain great practical advantages, as shown in (1) and (2) below; and obviates the difficulty of drawing an ellipse.